Problem: Simplify the following expression: $p = \dfrac{-35r}{42r^2}$ You can assume $r \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-35r = - (5\cdot7 \cdot r)$ The denominator can be factored: $42r^2 = (2\cdot3\cdot7 \cdot r \cdot r)$ The greatest common factor of all the terms is $7r$ Factoring out $7r$ gives us: $p = \dfrac{(7r)(-5)}{(7r)(6r)}$ Dividing both the numerator and denominator by $7r$ gives: $p = \dfrac{-5}{6r}$